Simulation of Turbulent Mixing Effects on Essential NO x –O 3 –Hydrocarbon Photochemistry in Convective Boundary Layer

Featured Application: Turbulent Kinetics Model (TKM) expresses nonlinear kinetics and dynamics of chemicals on essential photochemistry in heterogeneous systems with an assumption of a photostationary steady state. Abstract: The turbulence kinetics model (TKM) describes an overall reaction rate for microscopic mass transfer phenomenon expressed as separation intensity, I s , in a turbulent reacting ﬂow. This study examines the effects of turbulent mixing in the convective boundary layer (CBL) on essential NOx–O 3 –Hydrocarbon photochemistry containing sources of NO and a surrogate reactive hydrocarbon. The modeling approach applies for all species except OH with an assumption of a photostationary steady state. The TKM results reveal principal ﬁndings as follows: (1) effects of turbulence on reaction rates lead to signiﬁcant segregations throughout most of the CBL in reaction pairs NO + O 3 , RH + OH and NO + HO 2 ; (2) segregations permit signiﬁcantly higher concentrations of NO and RH to build up and endure in the CBL than would occur for a non-turbulent atmosphere; (3) turbulent segregation inﬂuences limit and shift the ranges of NO and O 3 concentrations compared to the non-turbulent case; (4) while there are differences between the TKM results and those for a published Large Eddy simulation (LES) of the same chemical system, there are also strong similarities. Therefore, a future study remains to compare model results to observations if and when appropriately time-resolved measurements of reacting species are obtained.


Introduction
Natural and environmental engineering systems are considered to be homogeneous systems in which the distribution of matter in the system is neglected at microscopic molecular scale movements and is mainly influenced by macroscopic physical migration phenomena, which affect the reaction energy and rate of reaction. In the homogeneous system, the conversion rate of the chemical is controlled either chemically or kinetically. Generally, it is very complicated to calculate the nonlinear chemical reaction rate in the heterogeneous system, so it tends to be ignored or simplified when assuming the homogeneous system [1]. However, the interaction between two molecules where an actual reaction takes place in a real system is a heterogeneous system in which small microscopic molecular scale turbulent migration phenomena are considered to be important [1]. The asymmetric mixing process strongly controls the chemical reaction rate when the timescale of the chemical reaction is of the same order or faster than the turbulent timescale [1][2][3][4][5][6][7][8]. The chemical reaction rate requires intimate mixing of the species at the molecular-scale (microscale), while dispersion is effected primarily by large-scale turbulent eddies with a nonlinear cascade process resulting in micro-mixing [8].
The largest mixing scale in the turbulent reacting flow is represented by the turbulent Damköhler (D t ) (or non-dimensional reaction rate), which is a ratio of the turbulent time scale (τ t ) to chemical time scale (τ ch ). The D t affects the segregation between the species in the asymmetric mixing process related to the chemical reaction [9]. Especially, the segregation of the species represents the influence of incomplete mixing on the chemical reaction rate when the chemical reaction time scale is similar to the turbulent time scale (|D t | ≥ 1). If the chemical reaction is extremely slow relative to the mixing processes (|D t | 1), the reactants become effectively well mixed. Also, the reacting species remain segregated in the case of very fast chemical reactions relative to mixing (|D t | 1). In a heterogeneous system, it is limited to the overall reaction rate due to the microscopic mass transfer phenomenon and can be expressed as the separation intensity, I s [3][4][5]7]. The intensity of segregation I s clearly depends on the turbulent Damköhler number and it can be related to the concentration fluctuation c A c B and the mean concentrations C A and C B of the reactive species A and B; I s = c A c B / C A C B . The concentration fluctuation needs to be well specified because the turbulent mixing effect on the chemical reaction rate can be measured by the concentration fluctuation. The effective (nonlinear) reaction rate is varied with the concentration covariance (fluctuation) that is a measure of segregation between two reactants, is directly related to the micromixing phenomena, and then is lowered or enhanced depending on whether the covariance is negative (non-premixed reactants) or positive (premixed reactants). Thus, the effective reaction rates, R e , in terms of the covariance can be rewritten in terms of the intensity of segregation I s .
The turbulent mixing effect on the chemical reaction rate can expressed as a function of the intensity of segregation I s (I s = −1 for the complete segregation between the species, I s = 0 for the perfectly mixed species by the turbulence, and I s > 0 or I s < 0 for the enhanced or lowered reaction rate compared to the perfectly mixed case).
The reaction of NO and O 3 in the atmosphere should consider the effect of turbulence with D t ≥ 1 when the intensity of segregation is always negative in the situation where both species are introduced at opposite boundaries [10]. Large regional ozone studies have been carried out in the San Joaquin Valley (central California) [11], Southeastern United States [12][13][14][15], Lake Michigan [16], Northeastern United States [17,18], United States [19,20], eastern North America [21], Russia [22], and Australia [23]. In those areas, maximum ozone concentrations during the summer exceeded the O 3 national ambient air quality standard (NAAQS) of 70 ppb finalized by the USEPA in 2015. Ozone studies have led to the recognition that realistic representations of turbulent mixing processes are very important for air quality simulation.
The effects of incomplete mixing on the chemical reaction between two species such as NO and O 3 are potentially very important when the time scale of the chemical reaction is of the same order or faster than the turbulent time scale [3][4][5][6][7][8]10]. A 1-D Turbulent Kinetics Model (TKM) [10] is applied to study the NO x -O 3 cycle as a representative reaction system whose reaction rates are affected by turbulent mixing in the convective boundary layer (CBL). The TKM chemical kinetics expression is modified by a term containing the covariance of the reactant concentrations in order to account for the effects of turbulence. Other studies have extended the scope to a more complex chemistry mechanism containing a wide range of chemical time scales [24][25][26]. The vertical turbulent transport of trace reactive species (the O 3 -NO-NO 2 triad) in the CBL during daytime has been used in the Second-Order Model for Conserved and Reactive Unsteady Scalars (SOMCRUS) [24]. SOMSCRUS [27,28] is run to investigate reactive species in the CBL and to obtain continuous equilibrium profiles of turbulent fluxes and mean concentrations of reactive scalars (the O 3 -NO-NO 2 triad) in a steady-state CBL without shear [29]. Also, SOMCRUS is used to calculate time-varying continuous profiles of mean concentrations and vertical turbulent fluxes, variances and covariances of both passive and reactive scalars (the O 3 -NO-NO 2 triad) [24]. A system in a simulation with a 1-D coupled diffusion and chemistry model applies a second-order closure scheme in the neutral Atmospheric Boundary Layer (ABL) over a remote deciduous forest [26]. However, those studies used the mean reaction rate formulation of the chemical kinetics which neglected the contribution of the covariance term. The turbulent effect on chemical reaction rates has been studied for "essential" daytime photochemistry with hydrocarbons and with various chemical time scales in the CBL by means of a large eddy simulation (LES) [25]. Those results showed that turbulence played a relatively modest role in affecting the evolution of the reaction system. The present study has an originality to develop the computational turbulent kinetic model (TKM) for expressing nonlinear kinetics and dynamics of chemicals in heterogeneous systems. For validating TKM applicability, model simulations are run for essential NO x -O 3 -RH photochemistry in a convective boundary layer (CBL). The present study uses the turbulent kinetics model (TKM) [10] and a set of photochemical reactions [25] to simulate the effects of turbulence on the reaction rates and distribution of important species in the CBL. For this purpose, this study compare the TKM results to those of a box model (BM), a conventional kinetics model (CKM) and the LES model [25]. Also, this study aims at providing the results of a sensitivity analysis of the TKM to show the effects of changes in such important parameters as nitric oxide (NO) and hydrocarbon (HC or RH) emission rates, reaction rate constants, dry deposition velocity, exchange velocity, turbulent time scale, and initial concentrations of species.

Model Reactions
The TKM has been developed in the previous study [10] with the assumption of horizontally homogeneous and vertically heterogeneous CBL in a quasi-steady-state characteristic of a summer cloud-free daytime as shown schematically in Figure 1a for the CBL with coupled chemical kinetics [10]. The TKM includes an asymmetric turbulent transport process to explain the macromixing influence represented by top-down and bottom-up(TDBU) diffusion of two species using the concept of the asymmetric convective model(ACM) [30] presented in Figure 1b. Figure 1c reveals elements of the 1-D TKM structure: The source is expressed by an emission term, a transport process (vertical mixing by turbulence), a transformation process (photochemical reaction, thermal chemical reaction, removal by dry deposition process expressed by a sink term), and output.
In this study, the TKM is applied to the daytime essential NO x -O 3 -RH photochemical system [25] with the reactions listed in Table 1 and Figure 1d. The species in the system are ozone (O 3 ), the oxides of nitrogen (NO, NO 2 and HNO 3 ), the oxides of hydrogen (OH, HO 2 , H 2 O, and H 2 O 2 ), and a generic hydrocarbon (RH). All but HNO 3 and H 2 O 2 have lifetimes similar to or shorter than the turbulent time scale (667 s in this paper). A constant CO concentration represents all the carbon species that have long lifetimes compared to the turbulent time scale (e.g., methane and CO). Water vapor is considered to be present at a constant concentration [25]. The product species HNO 3 and H 2 O 2 are not reactive and their concentrations increase with time in the model simulations, which assume they are not removed by dry deposition. Although this mechanism is oversimplified in its representation of atmospheric chemistry, it contains most of the key features included in more detailed mechanisms. Thus, this chemical mechanism can be used to illustrate the qualitative features of the general hydrocarbon-NO x -O 3 chemistry in the troposphere. The mechanism consists of the reactions listed in Table 1 and Figure 1d.    For the present purposes, this study considers that the chemical processes start with the photolysis of O 3 and NO 2 (R 2 ). These and the reaction between NO and O 3 are responsible for maintaining much of the O 3 concentrations (see Reference [10]). However, the long-term behavior of NO (and thus of O 3 ) depends upon the more complex chemistry, the essence of which is embodied in reactions R 1 -R 11 listed in Table 1. This set of reactions and terminology are referred to as the essential daytime photochemistry in Reference [25]. The key to understanding the chemistry is the centrally important OH radical. The OH radical via R 4 and R 5 oxidizes hydrocarbons (CO and RH). The HO 2 radicals react with NO to regenerate OH and complete the cycle (R 6 ). The photolysis of O 3 generates O( 1 D) which subsequently reacts with water to form OH radicals. Both steps are represented in the essential chemistry mechanism by the single reaction R 1 . Termination of the reaction chain occurs via R 9 , R 8 and R 11 . The concentration of H 2 O is assumed to be constant since it is determined mainly by the physical hydrologic and meteorological conditions. Constant CO concentration represents CO itself and all the hydrocarbons that have long lives compared to the turbulent timescale (e.g., methane). The rate constant for the reaction of CO with OH (R 4 ) is taken to be that for CO alone. For the reaction of RH with OH (R 5 ), the rate constant is expressed as the product of the constant for the CO reaction with OH and a parameter f . Also, the chemistry of the reaction between RH and OH is simplified by assuming it produces HO 2 as the only product of importance to the chemical scheme. Pseudo-Steady-State Approximation in the development of turbulence (PSSAt) and Photostationary Steady-State Approximation in the chemical reaction (PSSAc) are assumed for OH and HO 2 radicals, which have very short lifetimes. Thus, the production and destruction of OH is determined by the longer-lived species and its concentration can be calculated from (see [25]):

Model Equations
The TKM describes the reactions which occur over a substantial range of chemical time scales in a dry CBL with turbulence driven by constant surface heat flux without cumulus convection when the growth of the CBL is ignorable during the afternoon in the summer months as shown in Figure 1a. Previously, the TKM has conducted a simple NO x -O 3 photochemistry study to quantitatively account for turbulence-induced incomplete mixing of two interacting chemical species [10]. In this study, the NO and O 3 fluxes are not opposite in sign, which means they both have net upward transfers, so they are diluted in the upper CBL due to entrainment of 'clean air' from the free troposphere.
Governing equations in the TKM are described using a concentration field splitting method (CSM) for an effective chemical reaction rate [33,34] and a non-local closure asymmetric convective model (ACM) for the vertical mixing scheme [30]. As a computationally simple scheme, as shown in Figure 1b, the ACM provides realistic simulation of vertical mixing in the CBL as mentioned in the Appendix A. The effective reaction rate related to the intensity of segregation I s can be calculated using the concept of the CSM which explains the possible states of mixing of the two species considering the concentration fields (the reactive species and their inert surrogates) in position and time. Based on the CSM considering the binary reaction between A and B, the hypothetical concentrations of inert species A I and B I are present in the same position and time with the reactive concentration of the reactive species A and B because the species A I , B I , A and B transport in the same convective flow of the CBL. Also, the concept of a local phenomenal extent reaction ξ incorporates both stoichiometry and diffusion effects simultaneously in space and time. To reduce the number of partial differential equations needed to describe the evolution of multimolecular systems in the turbulent (incompletely mixed) field, the stoichiometric relations are combined with the concept of inert surrogate concentrations (see References [10,30,31] for details). Therefore, the mean concentration of the reactive species The governing equations of variables in the TKM for inert species, for reactive species, and for phenomenal extent of reaction ξ are time-dependent, nonlinear and coupled partial differential equations, which are expressed in a fixed Eulerian framework as given below (see Reference [10] for details): where, term I is the local rate of change of the variables, term II is the vertical turbulent flux transport, term III is the source and sink term, and i is the species A and B. The source term in term III is is the emission flux of species A at the surface level ∆z, or it is the entrained flux of species B at the top level ∆z. The effective reaction rate, R e c (ppb·s −1 ) for the sink term in term III is calculated for the mean phenomenal extents of reaction based on the CSM (see Section 2.3 for details). In this study, the mean concentration of reactive species is calculated using the inert surrogate mean concentration C I i and the phenomenal extent of reaction ξ instead of using Equation with the current time step m and the next time step m + 1 and the time difference ∆t between m and m + 1.

Model Approaches
The major governing equations solved in the TKM are the same as those described in the previous study [10]. The symbols and subscripts have, in general, the same meanings, but now the subscript i denotes species NO, O 3 , NO 2 , RH, HO 2 , and OH, and subscript j denotes the partner of species i for chemical reactions detailed in Table 1 (e.g., for NO in a reaction, R 3 , i = NO and j = O 3 ). Similarly, the source, sink and reaction rate terms are formulated to account for surface sources of NO and RH, dry deposition removal of species, entrainment of species from the free troposphere above the CBL, and the reactions listed in Table 1. The overall effective reaction rate (ppbv·s −1 ) for species i is where R k represents an individual reaction and subscript k denotes reaction number in Table 1 for all reactions of species involving species i. For example, the overall effective reaction rate of the species NO is The individual reaction R k between species i and j is expressed in terms of the segregation coefficient I s ij as where I I s ij is the intensity of segregation for inert species I I s ij = c I i c I j / C ; and ϕ ij is the reaction parameter as below: and c I i c I j is the concentration covariance of inert species i and j. The concentration variance and concentration covariance of inert species i and j are expressed by Equations (8) and (9), respectively. I  II  III  IV where, term I is the local rate of change, term II is the vertical turbulent flux transport processes, term III is the mean gradient production processes, and term IV is the molecular dissipation of the mean concentration variance and covariance for inert species i and j and of the mean concentration covariance for reactive species i and j [ppb 2 ·s −1 ] (refer to Reference [10] for details).

Simulation Description
For the TKM simulations, this study adopted the initial and boundary conditions and the parameter values from the Reference [25] for typical conditions of a continental boundary layer during daytime in summer. This study assumed the temperature to be constant at 298 K and the water vapor to have a concentration representing a relative humidity Rh = 45 %. Table 2 lists all of the conditions and assumptions used in the simulations. Homogeneous initial concentrations in the CBL were calculated from the chemical steady state using the Box Model (BM). At the surface, all species are removed according to their respective deposition velocities. The previous study [25] used a value of the dry deposition velocity for O 3 and NO 2 estimated from the study [35] and took arbitrary values for the other species. However, the dry deposition velocity for NO [25] is large (0.2 cm·s −1 ) compared to that of other studies [26,36]. Based on the previous studies, this study assumed a value of the deposition velocity for NO of 0.02 cm·s −1 [26] and the following surface emission fluxes [25]: For NO, 0.1 m·s −1 , and for RH, 1.0 m·s −1 . The NO emission flux is typical of an agricultural area and that of RH (all reactive hydrocarbons and intermediates) is based on isoprene flux determinations [37]. The flux at the top of the CBL is calculated using the exchange velocity w e , which is equal to 0.01 cm·s −1 , and the concentration differences between the top layer of the CBL and the free troposphere (FT); thus, exchange flux = w e (C CBL − C FT ). As indicated previously, the end-product species HNO 3 and H 2 O 2 are assumed to have zero deposition velocity.] Numerical simulations are carried out for the full governing equations using a forward time finite difference scheme. Concentrations, concentration variances, concentration covariances, fluxes, and the reaction parameters are computed using a grid spacing (64 grid points) distributed uniformly in altitude between the surface and the top of the CBL (Z i = 1000 m height). A time step of 1.5 s was used for all simulations, which lasted for 200 min in the model domain.

Comparison Description
Because there are no observational data suitable for validating our model and those of other models mentioned in this paper, this study compares the TKM model results to those of the 3-D LES model [25] and to several simplified model variants, as listed below and described in Table 3. • 0-D Box Model (BM) including chemical reactions and physical processes (emission, exchange of fluxes, and dry deposition process) but no convective transport and turbulence. • 1-D Conventional Kinetics Model (CKM) using mean reaction rates and including transport and turbulence. • 1-D Turbulent Kinetics Model (TKM) including transport and turbulence and using effective reaction rates.
The models operated with the same boundary and initial conditions (see Table 2) and rate constants (see Table 1). To calculate the deposition in the box model (BM), the box model concentration is used, and in the CKM and TKM, the deposition terms are calculated using the concentration in the lowest model layer.

Conditions
All the same conditions described in

Inerts
The TKM simulates the turbulent effect on chemical reaction rates by means of the concentration fields splitting method (CSM) using the extent of reaction [10]. In each simulation using the TKM, the inert species' concentrations are first computed by setting all reaction rates equal to zero. (The reader is reminded that the term "inert" as used here refers to a model pseudo-species and not to real unreactive substances. The 'inert' species calculation is for the same species but taking account only of their dispersion and not of the chemical reactions between them.) Then the model species' concentrations are computed. The inert case is used to calculate indirectly the extent of reaction and also is used as a control to indicate the effects of chemical reactions on the resulting concentration profiles. The integration of the governing equations is explained in the previous study [10].
The results of the TKM for the inert species are shown in Figure 2. Their vertical profiles reveal the effects of the physical processes in the ACM. For the bottom-up diffusing concentrations of inert species NO and RH, the vertical concentration profiles were very simple and constant throughout the CBL above the surface layer as shown in Figure 2a Figure 3 shows the computed vertical concentration profiles of the reactive species in the TKM from 10 through 200 min. Rapid convective transport in the model gives rise to nearly uniform vertical concentration profiles while continued surface emissions of RH ensure that its concentrations increase steadily with time. The temporal variations of NO concentrations are more complex, as will be discussed below. The large gradients for most species near the upper and lower boundaries are due to the physical processes of emission and entrainment fluxes, surface removal, and the rapid upward convection. Figure 4 shows the temporal behavior of the six reactive species and the two end-product species H 2 O 2 and HNO 3 for each of the surface, middle and top layers of the model. Here the complex early-time behavior of most of the species is clearly evident. The concentrations of the end products, H 2 O 2 and HNO 3 , increase monotonically out to 200 min because, in this simulation, they are created but not lost from the CBL. Their concentrations at a given time can thus be used as indications of the cumulative amounts of chemical processing.    During the first 20 min of model time, the chemical development proceeds as the emitted NO quickly starts to fill the CBL; its concentrations rise in all layers while photolysis of NO 2 serves to increase both NO and O 3 concentrations. The increase in O 3 concentrations leads to an increase in OH concentrations. This and the increasing RH concentrations lead to increasing HO 2 concentrations except in the top layer. There, the increasing NO concentrations and decreasing RH concentrations result in initially decreasing HO 2 concentrations via R 5 and R 6 . At about 10 min, the HO 2 concentrations begin to increase slightly and to reach a local maximum at about 15 min. Since the HO 2 concentration is computed from the PSSAc, the behavior of HO 2 in all layers can be rationalized by examining the temporal variations of the four non-radical reactive species in Figure 4 and referring to Table 1. The same is true for the OH behavior in time. Entrainment of air from the free troposphere causes the decreasing O 3 and RH concentrations in the top layer. Note that the concentration differences in the middle layer over the interval of 0-20 min are about equal but opposite for NO and NO 2 .

Reactive-Species Concentrations
After 20 min, the NO concentrations decrease in all layers because of reaction with O 3 ; thus resulting in increases in NO 2 concentrations after the latter reach minima at 20 min. Concurrently, O 3 concentrations start to decrease at similar rates in all layers. The NO concentrations reach minima in all layers at times varying from about 40 min for the top layer to about 70 min for the surface layer. A comparison of NO and NO 2 concentration differences over appropriate intervals reveals that the stoichiometric changes for NO 2 are a little larger than for NO. For example, in the middle layer, the NO concentration decreases by about 0.05 ppb in the interval of 20-70 min, while the NO 2 concentration increases by about 0.07 ppb. During the same interval, the concentration of HNO 3 increases by more than 0.2 ppb. It is seen that a major portion (roughly about 2/3) of the NO emissions up to 70 min gets processed to HNO 3 . This estimate does not take into account the effects of dry deposition of NO and NO 2 .
For times greater than about 60 min NO, NO 2 and RH concentrations in all layers increase steadily while O 3 , OH and HO 2 concentrations continue the decreasing trends that started after their respective early maxima. All of these changes can be understood as being driven by the emissions of NO and RH. A comparison of NO and NO 2 concentration differences over the 60-200 min. interval shows that the stoichiometric changes for NO 2 are much larger than for NO, e.g., in the middle layer where the NO concentration increases by about 0.04 ppb while the NO 2 concentration increases by about 0.22 ppb. Also during this period, the concentration of HNO 3 increases by 0.4 ppb. By 200 min, the proportion of total nitrogen species that is processed to HNO 3 is about 0.5 and the proportion of NO 2 is about 0.4 (neglecting dry deposition of NO and NO 2 ). Evidently, the continuing emissions of NO and RH overwhelm the ability of the oxidants to maintain their control of the growth of NO x . Another related result shown in Figure 4 is that by 200 min the concentration of NO in the top layer slightly exceeds that in the surface layer. This is due to both the rapid transport of NO from the surface and the fact that the photolysis rate of NO 2 exceeds that of the reaction of NO with O 3 by about 8 %.
Later this study will compare the TKM results to those for other model systems to illustrate the differences caused by turbulence effects.

Reactant Segregation
When the chemical reaction timescale is of similar magnitude to or smaller than the turbulence timescale (τ ch ≤ τ t ), segregation of reactants becomes significant (I s > 0 or I s < 0); thus, the reaction rate enhances or retards. Since the coefficient of segregation, I s , of a reaction is exactly the dimensionless (relative) covariance of the concentrations of the reactants, its value is positive when both reactants have collocated sources and is negative when the reactants originate from sources affected mainly by opposed motions. Figure 5a shows, via the coefficient of segregation, the effects of turbulence on the reaction rates as simulated in the TKM for the reactions detailed in Table 1 (e.g., the segregation between NO and O 3 , between NO and HO 2 , and between RH and OH, etc.). Even though the chemical reaction chains tend to cause a balance between the production and the destruction of several species, large segregation appears for reactions involving the emitted species NO and RH. These effects permit the NO and RH concentrations to increase continuously after the early periods of decrease as discussed above. In the following discussion, the important reaction pairs have negative segregation coefficients. We will refer to their absolute values in percent, so that a minimum value in I s is referred to as a maximum segregation. The vertical profiles (Figure 5a Table 1 (e.g., the segregation between NO and 403 O3, between NO and HO2, and between RH and OH, etc.). Even though the chemical reaction chains 404 tend to cause a balance between the production and the destruction of several species, large 405 segregation appears for reactions involving the emitted species NO and RH. These effects permit the 406 NO and RH concentrations to increase continuously after the early periods of decrease as discussed 407 above. In the following discussion, the important reaction pairs have negative segregation 408 coefficients. We will refer to their absolute values in percent, so that a minimum value in Is is referred 409 to as a maximum segregation. The vertical profiles (Figure 5a)   Comparing the TKM to three other models further shows the effects of turbulence on the 432 photochemical system in the CBL. The models and their characteristics are listed in Table 3. In order 433 of complexity, these are a chemistry-only box model (BMCh), a box model (BM) and a chemical emission, deposition and exchange between CBL and free atmosphere. The chemical processes are 440 the full set of reactions given in Table 1. Since there is no turbulence and only one compartment of 441 the CBL, the chemical kinetics terms contain only the mean concentrations. The BMCh represents 442 only photochemistry with no emissions of NO and RH. There are no physical processes, viz. emission, 443 deposition, exchange, transport, and turbulence. As the photochemical reactions proceed,

453
The TKM results shown in Figure 6 are the same as those for the middle layer shown in Figure  454 4. The differences between the CKM and the TKM are attributable to the retarding effects of 455 turbulence on the important reaction rates, because in the CKM, Is = 0. Thus, the large early 456 segregation between NO and O3 (see Figure 5b)

Comparisons with Other Models
Comparing the TKM to three other models further shows the effects of turbulence on the photochemical system in the CBL. The models and their characteristics are listed in Table 3. In order of complexity, these are a chemistry-only box model (BMCh), a box model (BM) and a chemical kinetics model (CKM). The results of the simulations for the middle layer of the CBL are shown in Figure 6. Since the box models have no dimensionality, the results shown in Figure 6 are merely the single sets of concentrations computed in the models. The initial concentrations of species are those of Krol et al. [25], and these were used in each simulation. The BM maintains a balance of physical and chemical processes, considering the whole CBL as a box. The physical processes simulated are emission, deposition and exchange between CBL and free atmosphere. The chemical processes are the full set of reactions given in Table 1. Since there is no turbulence and only one compartment of the CBL, the chemical kinetics terms contain only the mean concentrations. The BMCh represents only photochemistry with no emissions of NO and RH. There are no physical processes, viz. emission, deposition, exchange, transport, and turbulence. As the photochemical reactions proceed, concentrations of NO and NO 2 decrease toward zero. The CKM has all of the features of the TKM except I s = 0. Thus, it represents the usual approach to transport and chemistry using only average concentrations of species in the reaction rate expression. Except for O 3  The TKM results shown in Figure 6 are the same as those for the middle layer shown in Figure 4. The differences between the CKM and the TKM are attributable to the retarding effects of turbulence on the important reaction rates, because in the CKM, I s = 0. Thus, the large early segregation between NO and O 3 (see Figure 5b) combined with photolysis causes the NO 2 concentrations to decrease and keep NO concentrations higher than for the CKM. The early photolysis of NO 2 contributes to the increase in O 3 and OH concentrations and thus, retards the rise of RH concentrations. However, NO-O 3 segregation, combined with the continued emissions of RH along with 50 % segregation between RH and OH, ultimately chokes off the HO x and NO x cycling reactions. This prevents the O 3 concentrations from increasing as they would in the CKM. Thus, the choking-off effect leaves the NO and NO 2 concentrations higher than in the CKM while the O 3 concentrations are lower. All of this is reflected also in the lower rates of buildup in the TKM of H 2 O 2 and HNO 3 cumulative concentrations.
Another set of model simulations was carried out to compare the TKM with the CKM for the reversible NO x -O 3 system [10]. In the analysis below, we also compare the results with those obtained for the NO x -O 3 -RH system. All simulation conditions in the models are the same except for the chemical mechanisms. As in the previously discussed TKM and CKM simulations, initial concentrations are 68.8 ppbv of O 3 and 0.138 ppbv of NO. Figure 7 shows the results in the form of NO-O 3 time trajectories for the bottom, middle and top layers of the CBL. Clearly the NO x -O 3 -RH chemical mechanism (triangle) shows markedly different behavior from the simple NO x -O 3 case (diamond). The results for the NO x -O 3 -RH system are the same as previously discussed, but are presented here from a different perspective. The striking feature is that the trajectories for the CKM have distinctly different shapes and tendencies from those of the TKM in all layers. This is yet another way of portraying the segregation effects on the NO-O 3 reaction pair. They act to separate the ranges of variability of NO concentrations and to produce slightly overlapping ranges of O 3 concentrations. By contrast with those for the NO x -O 3 -RH system, the TKM and CKM trajectories for the NO x -O 3 system, while showing early differences, are quite similar in all layers for later times. In the top layer they become parallel, separated by about 0.2 ppb NO at any time after about 20 min. The tendencies for parallel behavior are evident in the bottom and middle layers, but they approach it at later times. From the foregoing and Figure 7, it is evident that in the TKM the effect of RH sources when added to the NO sources is to constrict the range of variability of NO and O 3 concentrations.
Finally, we compare the TKM with the LES simulation [25] of the same chemical mechanism. The fundamental differences in the two approaches lie in their dimensionality (three vs. one), atmospheric dynamics, sub-grid scale parameterization, and initial times and conditions for simulation. These differences impede detailed comparisons. However, the relatively uniform vertical distributions of species and segregation coefficients and the time evolution of intensity of segregation for R 3 have significant similarities. The LES results for uniform source distribution provide generally significantly lower segregation intensities than the TKM. The TKM produced similarly low values in the sensitivity analysis when the molecular time scale was increased. Since the Damköhler number is the appropriate scaling parameter for comparing intensities of segregation, decreasing the turbulent time scale (τ t ) in the TKM would also produce similarity. However, the value of τ t of 11 min was chosen in the TKM to be the same as in the LES. It is difficult to point to any single quantity that may account for the differences, but it seems quite probable it lies in the parameterizations that exist in both models rather than in a fundamental difference in the physical and chemical processes represented in them. There remains the difficult task of performing adequately time-resolved concentration measurements of reacting species in the turbulent convective boundary layer to determine if and to what extent turbulent segregation occurs. system, while showing early differences, are quite similar in all layers for later times. In the top layer 479 they become parallel, separated by about 0.2 ppb NO at any time after about 20 minutes. The 480 tendencies for parallel behavior are evident in the bottom and middle layers, but they approach it at 481 later times. From the foregoing and Figure 7, it is evident that in the TKM the effect of RH sources 482 when added to the NO sources is to constrict the range of variability of NO and O3 concentrations.   Table 4 lists the parameters that were varied along with their values used in the sensitivity analysis of the TKM. The reference case is that which we have discussed above. Figure 8a,b show respectively the results of the sensitivity analysis in terms of the concentration ratios to the reference case of the six principal species and the coefficients of segregation (I s ) of six principal reactions at 90 min of simulated time. Note the scale changes among the plots and particularly that the OH and HO 2 concentrations scales are logarithmic.  Table 4 and (b) segregation sensitivity for the parameters detailed in Table 4.

517
The sensitivity analysis reveals the following: 518 • The concentrations of OH and HO2 varied the most (relative to the reference case concentrations) 519 of any other species modeled in the TKM. This is because the mechanism for the oxidation of RH 520 and cycling of NOx involves chain reactions with the HOx radicals as the principal intermediates at 521 very low concentrations between the much more abundant emitted species and their end products. 522 • The concentrations of NOx, HOx and RH modeled in the TKM were most sensitive to changes in the 523 emission rates of NO and RH. 524 • Because the initial concentrations of O3 are much larger than for the other species, they varied on 525 an absolute basis more than any species except RH. However, because the reaction scheme is 526 cyclical for O3, it varied little relative to the reference case. 527  Table 4 and (b) segregation sensitivity for the parameters detailed in Table 4.
The sensitivity analysis reveals the following:

•
The concentrations of OH and HO 2 varied the most (relative to the reference case concentrations) of any other species modeled in the TKM. This is because the mechanism for the oxidation of RH and cycling of NO x involves chain reactions with the HO x radicals as the principal intermediates at very low concentrations between the much more abundant emitted species and their end products.

•
The concentrations of NO x , HO x and RH modeled in the TKM were most sensitive to changes in the emission rates of NO and RH.

•
Because the initial concentrations of O 3 are much larger than for the other species, they varied on an absolute basis more than any species except RH. However, because the reaction scheme is cyclical for O 3 , it varied little relative to the reference case.

•
The segregation effects of turbulence on R 5 and R 6 were promoted by increased emission rates of RH and NO, respectively. Decreased emission rates of those species diminished the effects of turbulence.
• The concentrations of the major species and the segregations of the principal reactions produced by the TKM appear to be relatively insensitive to the specific hydrocarbon mechanism as judged by comparing the CB-4 to the reference case [36]. Significant differences appear in HO x species and could be expected in their end products, H 2 O 2 and HNO 3 , especially at later times.

Conclusions
The TKM successfully incorporates the "essential" chemical system using a generic hydrocarbon, RH, in conjunction with NO x and O 3 for a typical rural agricultural regional atmosphere with RH having the same reactivity with OH as isoprene. The transport scheme in the TKM assures that significant concentration gradients exist only near the upper and lower boundaries of the CBL. Emissions of NO and RH and dry deposition of species cause gradients near the surface. The turbulence represented in the TKM produces significant segregation in the three reaction pairs among eleven reactions NO + O 3 , NO + HO 2 , and RH + OH for times up to 200 min. As represented in the TKM, turbulence in the CBL allows for build-up of significantly higher concentrations of NO, NO 2 and RH, while preventing the increase in O 3 concentrations compared to the CKM, in which the reactions proceed with no segregation due to turbulence. The similarity between the CKM results and those of the simple box model (BM) are nearly identical. This provides justification for the application of box model chemistry to represent the behavior of the boundary layer when turbulence effects are not included. However, the present study with the TKM indicates that turbulence effects should not be ignored in the convective boundary layer. Comparisons of the TKM with LES results are difficult because of differences in model structure and parameterizations. The LES gives lower coefficients of segregation for the principal reactions, thus representing the relatively small role of turbulence in affecting reaction rates. The TKM produces results similar to the LES for an increased molecular time scale, or equivalently, a decreased turbulent time scale. The sensitivity analysis, in which several model parameters and boundary conditions were varied, revealed less than linear changes in concentrations of the major species from changes in RH and NO emission rates. Lower emission rates lead to lower segregation effects in the principal reactions involving RH, NO and NO 2 . The concentrations of the intermediate radicals OH and HO 2 are more sensitive to the variations than the more stable and abundant species. However, changing the chemical mechanism from the "essential chemistry" to CB-4 leads to relatively small changes in species concentrations and reaction segregations. Finally, it would be desirable to have a set of high-resolution time-concentration data of the key species in the CBL to provide critical comparison with the TKM and the LES model. Using the vertical coordinate system defined as Ma, definitions of upward (M u ) and downward (M d ) mixing rates are essential to understanding the tendency equations in the ACM, and how it conserves air mass. With this understanding, ACM can be used to mix any quantity that is conserved during air transport and changes during mixing in proportion to the masses of the parcels that mix. The upward mixing rate can be defined as the rate of fractional mass flux in kg air from the lowest layer (k = 1) into any layer above per kg air in the upper layer per sec and estimated by convective velocity scale w * and mixing height Z i depending upon the sensible heat flux H 0 ; Also, the downward mixing rate (M d ) can be defined as the rate of fractional mass flux in kg air from layer k per kg air in layer k down to layer k-1 per second.
where, MaS k is the sum from j = k to j = kh of Ma j , kh is the top layer of the model layer, Ma k is the mass of air in layer k, and z k represents the thickness of layer k, which is equal to z k − z k-1. Because the mass influx to the lowest model layer is from the second layer only in the ACM, the flux-form diffusion algorithm can be written for the lowest layer (k = 1) as deposition height, h dep = ∆z 1 = Ma 1 /ρ L 1 , V d is the dry deposition velocity, ρ L 1 is the air density in layer 1, F i s is the flux through the bottom of the layer 1 for species i (ppb m s −1 ), F i 1 is the flux through the top of the layer 1 for species i (ppb·m·s −1 ), M u is the upward mixing rate (s −1 ), M d is the downward mixing rate (s −1 ), and MaA is the air mass summed from j = k = 2 to j = kh of Ma j (kg·m −2 ), In layer k > 1, the concentration variables in height-coordinate system are where, i is the inert species, the phenomenal extent of reaction, and concentration variances of the inert species, Ma is the air mass of layer k+1 and k in a numerical model (kg·m −2 ), M u is the upward mixing rate (s −1 ) and M d for the downward mixing rate (s −1 ).